If two electrons were to approach each other

I was wondering if two electrons were to approach each other, and if we regard electron as having wave-like properties, then, there is a chance that destructive interference will occur, which translates to the destruction of both electrons!?

Not the destruction of them -- just the lack of any probability for them to be at the place where they detructively interfere. Keep in mind the "wave" nature of all particles is a description of their probability to appear at a given point in space.